How about some extra endorphins?

by Michael Seckler

“From a biochemical perspective happiness is nothing more than the release of endorphins in the brain. Love, music, a nice sculpture or chocolate can cause that, but also complex mathematical constructs”. If math professor Christian Hesse was telling the truth in his interview with good impact magazine we seem to miss out on loads of endorphins all the time. Noort Bakx showed it with dating the other day: There is more math in your everyday-life than you might expect. You don’t think so? Maybe a look at this extremely average Wednesday of mine can convince you of the contrary (Do I already sound like the math teacher you hated? Good!): 

The Travelling-Salesman-Problem (Picture: dogonews.com)

The Travelling-Salesman-Problem (Picture: dogonews.com)

The day started – quite shockingly – with a coffee after waking up. Even though still 100% incapable of making mathematical decisions I was faced with one: If the coffee is too hot and I want it to cool down as fast as possible, when do I add the (cold) milk? Right away or only after a few minutes? If you say that it doesn’t matter, because the coffee cools down consistently, why doesn’t it freeze at some point? This graph has the answer:

Newton's Law of Cooling

Newton’s Law of Cooling

The curve describes the temperature loss over time. And you can see: It’s better to wait for a bit. During the first two minutes the coffee temperature sinks fast, even without the milk. Adding it right away would be “waste”. If you add it later on, however, the gain in time is bigger. No need to mention that I did it wrong. Moving on.

After my perfectly-tempered coffee I went to the supermarket and the bank. Since I wanted to sit and work in a café afterwards, I asked myself how to plan the tour: The supermarket is kind of on the way to the café, but also not really. The bank again is somewhere completely different. Obviously I didn’t get the map out and started planning my “trip”. But I could have. Algorithms help to optimize movements in similar situations all the time, regardless of whether it’s about the logistics of postmen, ships or satellites. I decided that I am neither of those and started walking on an completely non-optimized route towards the café.

Having arrived there I got my laptop out and began to work on something deeply a-mathematical. So finally a math-break? Nope. Since I’m still the owner of an prehistoric 4-kilo-laptop, I always dedicate some time to admire the beauty of newer models around me. How can an apple look so damn good? Some say that the answer lies partly in math, namely  “the golden ratio” which apple implemented in their design. You probably know it from art or architecture but let’s just quote wikipedia for a second: “Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities “.

Golden Ratio

This special point has reached a somewhat mythical status in mathematics and beyond. Mathematicians of the ancient world already discovered the golden ratio and it’s assumed characteristic of being the aesthetically ideal point of division. However, the question whether this ratio actually deserves its almost supernatural status is controversial; clear evidence for a special psychological effect is lacking. On top of this the theory of apple’s use of the golden ratio is hardly more than a vague assumption. For more certainty you better dedicate your star-shaped Christmas-cookies a closer look:

5 & 8 as well as 13 & 21 are in the golden ratio  (picture: http://der-goldene-schnitt.blogspot.de/)

5 & 8 as well as 13 & 21 are in the golden ratio
(picture: http://der-goldene-schnitt.blogspot.de/)

Talking of Christmas: I apparently went to the wrong café as they decided to play “last Christmas” at some point. In a moment of procrastination and Wham-emotions I started to scribble on my writing pad, drawing the “house of Santa Claus”. It’s a simple game in which you are asked to draw the house of Santa Claus in one line, without coming about one side twice.

The House of Santa Claus

The House of Santa Claus

However this time, it didn’t work. 10 minutes of scribbling, procrastination and googeling later, I realized that it is impossible to start from the middle or top point. You have to start from the bottom points because of the unequal number of lines running together there. The man behind this insight is Leonhard Euler, a Swiss mathematician from the 18th century.

I think, for now I should let you off the hook. However, my day surely offered more maths: Game Theory for example: Should I go to watch Champions-League on the danger that nobody will come, or just join the rest for dinner?

But enough, I think you get the point. Christmas is coming up and you’ll probably won’t suffer from chocolate-endorphin-shortage. So if you ever feel like adding some math-endorphins, all you need to do is giving your everyday-behavior a closer look.


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